Effect of Temperature on Adhesion Work of Model Organic Molecules on Modified Styrene–Divinylbenzene Copolymer Using Inverse Gas Chromatography

Abstract

In previous studies, a new methodology was developed to determine the free dispersive and polar energies, the surface energies, and Lewis acid–base parameters of a polystyrene–divinylbenzene (S-DVB) copolymer modified by melamine, 5-Hydroxy-6-methyluracil, and 5-fluouracil. In this paper, we were interested in the determination of the work of the adhesion of solvents on the modified copolymer as a function of temperature and for the different modifiers with the help of inverse gas chromatography at infinite dilution. The variations in the London dispersive and polar surface properties of copolymers against the temperature led to the determination of the different acid–base components of their surface energies. Using Fowkes’s equation, van Oss’s relation, and Owens’s concept, we obtained the variations in the dispersive and polar works of the adhesion of the different solid surfaces, and the corresponding forces of interaction between the organic solvents and the modified copolymer. It was shown that the work of adhesion is a function of two thermodynamic variables: the temperature and the modifier percentage.

1. Introduction

The study of surface interactions between polymers and solvents is fundamental in many technological and industrial applications such as adsorption, swelling, diffusion, composite fabrication, coatings and adhesives to membrane separations, and adhesion. Polymer surfaces and interfaces play an essential role in many commercial applications of polymers, such as coatings, adhesives, blends, packaging, resists, building, engineering, and biomedical industries. Understanding the interaction processes taking place at interfaces is, therefore, increasingly important for the wide variety of polymer uses.

In recent years, significant progress has been made in the regulation of polymer interfaces through advanced modification techniques and surface engineering strategies. For example, surface grafting, plasma treatments, and the incorporation of supramolecular architectures have been widely employed to tailor interfacial energies and adhesion properties of polymeric materials [1,2,3,4]. The insight into the molecular origins of interface effects via dual-interface regulation in the framework of charge hopping offers new development paths for developing advanced energy materials with tailored electrical properties. Novel copolymerization approaches and functional group insertions have also been shown to drastically alter surface polarity and molecular interactions, improving compatibility with organic and bioactive molecules [5,6,7,8]. These advancements underscore the importance of molecular-level surface design in tuning adhesion and dispersion forces—principles central to the present study on 5-fluorouracil-modified S-DVB copolymers. Incorporating such knowledge helps align our methodology with broader efforts to develop polymer surfaces with controlled physicochemical properties for use in separations, biomedical applications, and responsive materials [7,8,9,10].

The most important parameter that governs such interfacial interactions is the work of adhesion (W_a), which quantifies the energy required to separate two phases in contact, a solid or a liquid solvent, and a solid polymer surface [11,12]. Understanding the thermodynamics and molecular mechanisms that dictate solvent adhesion to polymer or copolymer surfaces is essential for controlling wettability, solvent uptake, film stability, and interfacial compatibility [13,14]. The strength of adhesion to a solid surface can be estimated from the value of the thermodynamic “work of adhesion”, $W_a$, a concept first introduced by Harkins [15] using the various surface tensions intervening when a liquid adheres to a solid.

The adhesion process was described in classical interfacial thermodynamics, using surface tensions and contact angle measurements and utilizing the work of Harkins [5] and the Young–Dupré equation [16,17]. Later, models were proposed by Fowkes [18], Owens–Wendt [19], and van Oss et al. [20,21], taking into account intermolecular forces, including dispersive, polar, and acid–base interactions [18,19,20,21]. These models provided a more comprehensive understanding of the thermodynamic equilibrium at the solid–liquid interface, especially when dealing with chemically complex or functionalized polymer surfaces.

Polymers and copolymers, such as polystyrene, polymethyl methacrylate (PMMA), and styrene–divinylbenzene (S–DVB) resins, exhibit different chemical functionalities, crosslinking densities, and very interesting morphologies. These properties play a key role in how solvents interact at the surface and in the bulk [22,23]. Moreover, the choice of solvent, characterized by its polarity, hydrogen bonding capacity, and molecular size, directly influences its adsorption behavior and the resulting adhesion energy [23,24]. The synergy between solvent properties and polymer surface energetics thus determines the degree of solvent penetration, polymer swelling, and final desorption dynamics [25].

Despite the crucial role played by adhesion, a rigorous understanding of solvent–polymer adhesion remains elusive due to the complex interplay of a large number of physical, mechanical, thermodynamic, and chemical factors. However, recent advances in experimental techniques, such as contact angle goniometry, isothermal titration calorimetry (ITC), and inverse gas chromatography (IGC), have allowed for the more precise quantification of adhesion energies and provided a better understanding of solvent–surface interactions at the molecular level [12,22].

In this paper, we aim to provide a new way to determine the work of adhesion of solvents on the surfaces of polymers or copolymers, such as the polystyrene–divinylbenzene (S-DVB) copolymer modified by several molecules or supramolecules, which have had great success in biochemical and pharmaceutical applications. This study is based on the theoretical models that have been validated by experimental results such as the Hamieh thermal model [26,27,28,29,30,31] and the separation method of the London dispersive and polar free energy of adsorption [32,33], using the well-known inverse gas chromatography (IGC) technique [34,35,36,37,38,39,40,41,42,43,44] at infinite dilution. This research used our new results on the different surface properties of modified copolymers [45,46,47] to determine the work of adhesion of the various organic model solvents on the S-DVB copolymer versus the modifier percentage and the temperature.

2. Materials and Methods

2.1. Materials and Technique

The different organic solvents, such as n-alkanes and polar molecules, were purchased from Chimreactivsnab (Moscow, Russia), while the different modifiers (melamine, 5-HMU, and 5-FU) were purchased from Vecton, (St. Petersburg, Russia), and the styrene–divinylbenzene copolymer was obtained from Dow Chemical (Michigan, Midland, USA). The chromatographic measurements of the retention volume of the various organic solvents adsorbed on the modified S-DVB were carried out with a Chromos GC-1000 chromatograph (Chromos, Moscow, Russia) equipped with a flame ionization detector (FID). The solid particles were packed into stainless steel columns of 30 cm in length and 3 mm in internal diameter. The experimental procedure was the same as that developed in previous works [45,46,47]. The experiments were repeated three times and the error in the value of the retention volume was about 1%.

2.2. Thermodynamic Methods

2.2.1. Surface Energy Parameters of Modified Copolymers

The application of the Hamieh thermal model allowed us to obtain the correct London dispersive surface energy ${\gamma }_s^d\left(T\right)$ of the S-DVB copolymer, modified, respectively, by melamine [45], 5-hydroxy-6-methyluracil [46], and 5-fluouracil [47], for percentages varying from 1% to 10% and temperatures from 443.15 K to 473.15 K. The new applied methodology led to the separation between the dispersive free energy $∆G_a^0\left(T\right)$ and the polar free energy $∆G_a^p\left(T\right)$ of adsorption of the various organic molecules adsorbed on the modified S-DVB copolymer at different temperatures.

${\gamma }_s^p\left(T\right)$ denotes the polar surface energy of the modified copolymer, and the total surface energy ${\gamma }_s\left(T\right)$ can be written as follows:

$${\gamma }_s\left(T\right)={\gamma }_s^d\left(T\right)+{\gamma }_s^p\left(T\right)$$

(1)

Applying Van Oss et al.’s method [21] to the modified copolymers, we obtained the different values of the Lewis acid ${\gamma }_s^{+}$, and base ${\gamma }_s^{-}$ surface energies using the following expression of $∆G_a^p\left(T\right)$ and the well-known surface parameters of two polar solvents such as ethyl acetate and dichloromethane:

$$-∆G_a^p\left(T\right)=2\mathcal{N}a\left(T\right)\left(\sqrt{{\gamma }_l^{-}{\gamma }_s^{+}}+\sqrt{{\gamma }_l^{+}{\gamma }_s^{-}}\right)$$

(2)

Equation (2) led to the values of the acid–base surface energy ${\gamma }_s^{AB}$ or ${\gamma }_s^p$ of the solid surfaces with the help of Relation (3):

$${\gamma }_s^{AB}={\gamma }_s^{p }=2\sqrt{{\gamma }_s^{+}{\gamma }_s^{-}}$$

(3)

2.2.2. Surface Energy and Work of Adhesion

Considering a liquid of known surface tension ${\gamma }_l$ in contact with a simple solid, smooth, homogeneous, non-deformable, and isotropic surface, the corresponding work of adhesion $W_a$ can be then written as follows:

$${W_a=\gamma }_s+{\gamma }_l-{\gamma }_{sl}$$

(4)

where ${\gamma }_{sl}$ is the solid–liquid interface tension.

Young [48] proposed the following equation:

$${{\gamma }_l cos\theta =\gamma }_s-{\gamma }_{sl}$$

(5)

This was obtained by defining the concept of the contact angle $\theta$ formed between the liquid drop and the plan solid surface.

On the other hand, Dupré [17] used Young’s equation [48] and expressed the work of adhesion by Equation (6):

$$W_a={\gamma }_l \left(1+cos\theta \right)$$

(6)

Fowkes [18] applied the geometric mean of the dispersive components of the solid and liquid and proposed a new expression of the work of adhesion:

$$W_a={\gamma }_l \left(1+cos\theta \right)=2\sqrt{{\gamma }_s^{\mathrm{d}}{\gamma }_l^{\mathrm{d}}}$$

(7)

where Equation (7) is only valid for dispersive interactions.

Later, the Fowkes’s equation [18] was extended to an approach taking into account the polar contribution (hydrogen bonding) [19] in the expression of the work of adhesion:

$$W_a=2\sqrt{{\gamma }_s^{\mathrm{d}}{\gamma }_l^{\mathrm{d}}}+2\sqrt{{\gamma }_s^{\mathrm{p}}{\gamma }_l^{\mathrm{p}}}$$

(8)

The values of ${\gamma }_s^p$ and the Lewis acid ${\gamma }_s^{+}$ and base ${\gamma }_s^{-}$ surface energies of solid copolymers were obtained using Van Oss et al.’s method [10] and applying Equation (9):

$$-∆G_a^p\left(T\right)=2\mathcal{N}a\left(T\right)\left(\sqrt{{\gamma }_l^{-}{\gamma }_s^{+}}+\sqrt{{\gamma }_l^{+}{\gamma }_s^{-}}\right)$$

(9)

This allowed for obtaining the polar (or acid–base) surface energy ${\gamma }_s^{AB}$ of the modified copolymers using Equation (10):

$${\gamma }_s^{AB}={\gamma }_s^{p }=2\sqrt{{\gamma }_s^{+}{\gamma }_s^{-}}$$

(10)

Therefore, the work of adhesion can be expressed as follows:

$$W_a=2\left[\sqrt{{\gamma }_s^{\mathrm{d}}{\gamma }_l^{\mathrm{d}}}+\sqrt{{\gamma }_l^{-}{\gamma }_s^{+}}+\sqrt{{\gamma }_l^{+}{\gamma }_s^{-}}\right]$$

(11)

The different surface energy components of the modified copolymers were previously determined. The work of adhesion was then calculated with the help of Equation (11).

Furthermore, the dispersive $W_a^{\mathrm{d}}\left(T\right)$ and polar $W_a^{\mathrm{p}}\left(T\right)$ contributions of the work of adhesion can be determined using the following equations:

$$\left\{\begin{array}{c}{W}_a\left(T\right)=W_a^{\mathrm{d}}\left(T\right)+W_a^{\mathrm{p}}\left(T\right) \\ W_a^{\mathrm{d}}\left(T\right)=2 \sqrt{{\gamma }_s^{\mathrm{d}}{\left(T\right)\gamma }_l^{\mathrm{d}}\left(T\right)} \\ W_a^{\mathrm{p}}\left(T\right)=2 \left[ \sqrt{{\gamma }_l^{-}{\gamma }_s^{+}}+\sqrt{{\gamma }_l^{+}{\gamma }_s^{-}}\right]=2 \sqrt{{\gamma }_l^{\mathrm{p}}\left(T\right){\gamma }_s^{\mathrm{p}}\left(T\right)}\end{array}\right.$$

(12)

3. Results

3.1. London Dispersive Surface Energy of Modified Copolymers

Two principal methods were used in the literature to determine the London dispersive surface energy, both based on the Fowkes equation [18]. The first one was proposed by Dorris and Gray [49], correlating the work of adhesion $W_a$ to the free energy of adsorption by the help of the surface area $a$ of the adsorbed molecule and the geometric mean of the dispersive components of the surface energy of the liquid solvent ${\gamma }_l^d$ and the solid ${\gamma }_s^d$.

$$∆G_a^0=\mathcal{N}a W_a=2\mathcal{N}a \sqrt{{\gamma }_l^d{\gamma }_s^d}$$

(13)

where $\mathcal{N}$ is Avogadro’s number.

Dorris and Gray [49] then determined the ${\gamma }_s^d$ of solid surfaces using the following relation:

$${\gamma }_s^d={\displaystyle \frac{{\left[RTln\left[\frac{V_n\left(C_{n+1}{H}_{2(n+2)}\right)}{V_n\left(C_n{H}_{2(n+1)}\right)}\right]\right]}^2}{4{\mathcal{N}}^{2 }{a}_{-CH2-}^2{\gamma }_{-CH2-}}}$$

(14)

where $V_n$ is the net retention volume of the adsorbed n-alkane, $C_n{H}_{2(n+1)}$ and $C_n{H}_{2(n+1)}$ represent the general formula of two consecutive n-alkanes, $a_{-CH2-}$ is the surface area of the methylene group equal to 6 Ų, and ${\gamma }_{-CH2-}$ is the surface energy of the methylene group, which is given by the following:

$${\gamma }_{-CH2-}\left(\mathrm{i}\mathrm{n} \mathrm{m}\mathrm{J}/{\mathrm{m}}^2\right)=52.603-0.058 T \left(\mathrm{i}\mathrm{n} \mathrm{K}\right)$$

(15)

The critiques to this method were formulated by Hamieh’s works [26,27,28,29,30,31,32,33], which proved that the surface area of organic molecules varies as a function of temperature, and showed an important dependence of the surface area of methylene group a_-CH2- versus the temperature. Hamieh [26] gave an expression of $a_{-CH2-}\left(T\right)$ (in Ų with T in K):

$$a_{-CH2-}\left(T\right)={\displaystyle \frac{69.939}{{\left(563.02-T\right)}^{1/2}}}$$

(16)

This proved the non-validity of results obtained by several scientists [50,51,52,53,54,55,56,57] using the Dorris and Gray method.

The second method was that of Schultz et al. [58], which was almost identical to the method of Dorris and Gray [39]; both were based on the Fowkes relation [18], and used the following relation:

$$RTln Vn={\left({\gamma }_s^d\right)}^{1/2}\left[2\mathcal{N}a {\left({\gamma }_l^d\right)}^{1/2}\right]+C$$

(17)

where $C$ is constant. These authors supposed that the surface area $a$ and the dispersive surface energy of molecules are constant at any temperature and obtained a n-alkanes straight line whose slope led to the value of ${\gamma }_s^d$ of the solid.

This method was widely applied by many researchers [54,55,56,57,59,60,61,62,63,64,65], despite the inaccuracy due to the dependence of the surface areas of molecules on the temperature. The Hamieh thermal model [26] gave the expressions of the dependence of the surface areas and ${\gamma }_l^d$ of n-alkanes polar molecules against the temperature. It was then concluded that the methods of Schultz et al. and Dorris–Gray, supposing the surface area of solvent molecules are constant, are inaccurate and cannot be used to determine the London dispersive surface energy, nor to evaluate the specific interactions.

The expressions of the surface areas and the dispersive surface energy of n-alkanes and polar molecules obtained by the Hamieh thermal model against the temperature were used to determine the correct London dispersive surface energy of the different modified copolymers.

Based on the Hamieh thermal model [26,27,28,29,30,31,32,33,34] and the Fowkes equation [18], the representation of the variations in $RTln{V}_n\left(T\right)$ of n-alkanes adsorbed on the modified copolymers as a function of $2\mathcal{N}a\left(T\right){\left({\gamma }_l^d\left(T\right)\right)}^{1/2}$ led to the ${\gamma }_s^d\left(T\right)$ of the various copolymers versus the temperatures [45,46,47]. The results are plotted in Figure 1, where a decrease in ${\gamma }_s^d\left(T\right)$ was observed as the temperature increased. The highest London dispersive surface energy was obtained with 1% melamine/S-DVB, closest to the ${\gamma }_s^d\left(T\right)$ of the copolymer alone, while the lowest values were shown with 10% 5-HMU/S-DVB. An important difference in the ${\gamma }_s^d\left(T\right)$ of the copolymer behavior was found to be affected both by the modifier and its percentage. Figure 1 clearly shows a decrease in the values of ${\gamma }_s^d\left(T\right)$ of S-DVB when it was modified by 5-HMU or 5-FU, which is certainly due to the morphology change in the copolymer structure.

The different linear equations of ${\gamma }_s^d\left(T\right)$ that are a function of temperature are given in

Table 1. Equations of ${\gamma }_s^d\left(T\right)$ of S-DVB-L-285 varying the percentage of 5-hydroxy-6-methyluracil, the linear regression coefficients R², the London dispersive surface entropy ${\epsilon }_s^d$, the values of London dispersive surface energy extrapolated at 0 K and 298.15 K, and the temperature maximum $T_{Max}$, using the Hamieh thermal model.

Copolymer	$\mathbf{Equation} \mathbf{of} {\mathit{\gamma }}_{\mathit{s}}^{\mathit{d}}\left(\mathit{T}\right)$ (mJ/m2)	${\mathit{R}}^2$	$-{\mathit{\epsilon }}_{\mathit{s}}^{\mathit{d}}={\mathit{d}\mathit{\gamma }}_{\mathit{s}}^{\mathit{d}}/\mathit{d}\mathit{T}$ (mJ m−2 K−1)	${\mathit{\gamma }}_{\mathit{s}}^{\mathit{d}}(\mathit{T}=0 \mathbf{K})$ (mJ/m2)	${\mathit{\gamma }}_{\mathit{s}}^{\mathit{d}}(\mathit{T}=298.15 \mathbf{K})$ (mJ/m2)	${\mathit{T}}_{\mathit{M}\mathit{a}\mathit{x}}$ (K)
S-DVB	${\gamma }_s^d\left(T\right)$ = −1.105 T + 587.13	0.9980	0.835	587.13	257.7	531.4
1% Melamine/S-DVB	${\gamma }_s^d\left(T\right)$ = −0.907 T + 496.21	0.9972	0.907	496.21	225.79	547.1
2% Melamine/S-DVB	${\gamma }_s^d\left(T\right)$ = −0.656 T + 341.59	0.9590	0.656	341.59	146.12	521.0
3% Melamine/S-DVB	${\gamma }_s^d\left(T\right)$ = −0.827 T + 439.96	0.9608	0.827	439.96	193.51	532.3
4% Melamine/S-DVB	${\gamma }_s^d\left(T\right)$ = −0.876 T + 473.64	0.975	0.876	473.64	212.40	540.6
5% Melamine/S-DVB	${\gamma }_s^d\left(T\right)$ = −0.935 T + 501.23	0.9825	0.935	501.23	222.46	536.07
10% Melamine/S-DVB	${\gamma }_s^d\left(T\right)$ = −1.220 T + 584.42	0.9915	1.220	584.42	220.68	479.03
Copolymer	Equation of ${\gamma }_s^d\left(T\right)$ (mJ/m2)	$R^2$	${-\epsilon }_s^d={d\gamma }_s^d/dT$ (mJ m−2 K−1)	${\gamma }_s^d(T=0 \mathrm{K})$ (mJ/m2)	${\gamma }_s^d(T=298.15 \mathrm{K})$ (mJ/m2)	$T_{Max}$ (K)
1% HMU/S-DVB	${\gamma }_s^d\left(T\right)$ = −0.874 T + 444.68	0.9837	0.874	444.68	184.16	508.9
3.5% HMU/S-DVB	${\gamma }_s^d\left(T\right)$ = −1.096 T + 544.23	0.9886	1.096	544.23	217.52	496.7
5% HMU/S-DVB	${\gamma }_s^d\left(T\right)$ = −1.120 T + 552.77	0.9973	1.198	552.77	218.84	493.6
10% HMU/S-DVB	${\gamma }_s^d\left(T\right)$ = −1.198 T + 582.13	0.9973	1.198	582.13	224.95	485.9
Copolymer	Equation of ${\gamma }_s^d\left(T\right)$ (mJ/m2)	$R^2$	${-\epsilon }_s^d={d\gamma }_s^d/dT$ (mJ m−2 K−1)	${\gamma }_s^d(T=0 \mathrm{K})$ (mJ/m2)	${\gamma }_s^d(T=298.15 \mathrm{K})$ (mJ/m2)	$T_{Max}$ (K)
1% 5-FU/S-DVB	${\gamma }_s^d\left(T\right)$ = −0.497 T + 290.95	0.8900	0.497	290.95	142.77	585.4
5% 5-FU/S-DVB	${\gamma }_s^d\left(T\right)$ = −0.780 T + 424.67	0.9800	0.780	424.67	192.11	544.4
10% 5-FU/S-DVB	${\gamma }_s^d\left(T\right)$ = −0.913 T + 490.08	0.9900	0.913	490.08	217.87	536.8

, including the values of the surface entropy and the maximum temperature of the various modified copolymers. The results in Table 1 prove that there is a difference in the various surface thermodynamic variables of the modified copolymers. Furthermore, the abnormally high values of the London dispersive surface extrapolated at 298.15 K and observed in Table 1 are mainly due to the nonlinear variations in the ${\gamma }_s^d\left(T\right)$ of the solid surfaces for lower temperatures, which resulted in the important change in the surface groups of the copolymers when the temperature undergoes severe variations from 475.15 K to 298.15 K.

Table 1 shows that the different values of −${\epsilon }_s^d$, ${\gamma }_s^d(T=0 \mathrm{K})$ and ${\gamma }_s^d(T=298.15 \mathrm{K})$, increased when the percentage of 5-hydroxy-6-methyluracil increased. This also shows that there is an important effect of the surface groups of the copolymer on the London dispersive surface parameters. However, a decrease was observed in the values of $T_{Max}$ when the modifier percentage increased, which is certainly due to the decrease in ${\gamma }_s^d\left(T\right)$ for higher temperatures.

3.2. Polar (Lewis Acid–Base) Surface Energy of Modified Copolymers

First, the polar acid ${\gamma }_s^{+}$ and base ${\gamma }_s^{-}$ surface energies of modified copolymers were obtained using the method of van Oss et al. [20]. This led to the values of the polar surface energy ${\gamma }_s^p$ and consequently to those of the total surface energy ${\gamma }_s^{tot.}$ obtained as a function of temperature using the previous equations and the results of ${\gamma }_s^d\left(T\right)$. The values of ${\gamma }_s^p\left(T\right)$ of the copolymers are given in

Table 2. Variations in polar surface energy ${\gamma }_s^p\left(T\right)$ (in mJ/m²) of modified copolymers and the corresponding linear equations.

Temperature T (K)	453.15	458.15	463.15	468.15	473.15	$\mathbf{Equation} {\mathit{\gamma }}_{\mathit{s}}^{\mathit{p}}\left(\mathit{T}\right)$	R2
S-DVB copolymer	81.54	76.29	71.17	66.19	61.33	${\gamma }_s^p\left(T\right)$ = −1.01 T + 539.27	0.9998
1% Melamine/S-DVB	70.11	68.03	65.99	64	62.07	${\gamma }_s^p\left(T\right)$ = −0.40 T + 252.32	0.9998
2% Melamine/S-DVB	124.35	120.53	116.81	113.18	109.63	${\gamma }_s^p\left(T\right)$ = −0.74 T + 457.69	0.9998
3% Melamine/S-DVB	54.36	50.34	46.51	42.87	39.41	${\gamma }_s^p\left(T\right)$ = −0.75 T + 392.86	0.9991
4% Melamine/S-DVB	84.71	79.24	73.99	68.97	64.16	${\gamma }_s^p\left(T\right)$ = −1.03 T + 550.05	0.9994
Temperature T(K)	453.15	458.15	463.15	468.15	473.15	Equation ${\gamma }_s^p\left(T\right)$	R2
1% 5-HMU/S-DVB	36.89	35.08	33.04	31.34	29.61	${\gamma }_s^p\left(T\right)$ = −0.37 T + 202.7	0.9990
3.5% 5-HMU/S-DVB	73.56	69.12	63.85	59.40	54.90	${\gamma }_s^p\left(T\right)$ = −0.94 T + 499.9	0.9992
10% 5-HMU/S-DVB	78.82	74.47	69.42	65.06	60.66	${\gamma }_s^p\left(T\right)$ = −0.92 T + 493.28	0.9994
Temperature T(K)	453.15	458.15	463.15	468.15	473.15	Equation ${\gamma }_s^p\left(T\right)$	R2
1% 5-FU/S-DVB	23.61	21.01	18.60	16.35	14.28	${\gamma }_s^p\left(T\right)$ = −0.47 T + 234.78	0.9980
5% 5-FU/S-DVB	105.08	96.96	89.26	81.96	75.06	${\gamma }_s^p\left(T\right)$ = −1.50 T + 784.76	0.9990
10% 5-FU/S-DVB	98.84	93.37	88.12	83.08	78.23	${\gamma }_s^p\left(T\right)$ = −1.03 T + 565.47	0.9994

. They show that the modifier 2% melamine on the S-DVB copolymer exhibited the highest polar surface energy, followed by 5% 5-Fu/S-DVB. The lowest ${\gamma }_s^p\left(T\right)$ was observed with 1% 5-Fu/S-DVB. The results in Table 2 clearly show the significant effect of the temperature and modifier on the polar surface energy.

To highlight the effect of the modifier percentage on the ${\gamma }_s^p$ of the different modified copolymers, the curves of ${\gamma }_s^p$ of solid surfaces are plotted in Figure 2 as a function of the modifier percentage. The variations in ${\gamma }_s^p$ for all used modifiers are not linear when the modifier percentage varies. The results show a maximum of ${\gamma }_s^p$ at 2% melamine/S-DVB and a minimum at 3% of melamine for all temperatures with a pallier after 4% melamine (Figure 2a). However, a minimum of ${\gamma }_s^p$ was observed at 1% of 5-HMU (Figure 2b) and 5-FU (Figure 2c) for the different temperatures, and a pallier shown in Figure 2 after 4% of the modifier on the S-DVB copolymer. The results thus prove that the polar surface energy is strongly affected not only by the temperature but also by both the nature and the percentage of the modifier, as is shown in Figure 3. It seems that the S-DVB copolymer modified by melamine gives the highest ${\gamma }_s^p$ at 2% melamine, while the 5-FU on S-DVB exhibits the highest ${\gamma }_s^p$ after 4% 5-FU.

3.3. Polar Surface Energy of Organic Solvents

The polar free energy $-∆G_a^p\left(T\right)$ of the adsorption of solvents on the various copolymers can be also written as follows:

$$-∆G_a^p\left(T\right)=2\mathcal{N}a\left(T\right)\sqrt{{\gamma }_l^{\mathrm{p}}\left(T\right){\gamma }_s^{\mathrm{p}}\left(T\right)}$$

(18)

where ${\gamma }_l^{\mathrm{p}}\left(T\right)$ is the polar surface energy of the solvents depending on temperature and also on the nature of the solid surface.

The variations in $-∆G_a^p\left(T\right)$ of the various polar solvents versus the temperature were previously determined [45,46,47]. Knowing the values of ${\gamma }_s^{\mathrm{p}}\left(T\right)$ of the various copolymers and those of the surface area of the different organic molecules [26,27,28,29,30,31,32,33], the variations in ${\gamma }_l^{\mathrm{p}}\left(T\right)$ were directly obtained using Equation (18). The results are plotted in Figure S1. The curves in Figure S1 show linear variations in the ${\gamma }_l^{\mathrm{p}}\left(T\right)$ of the different polar solvents versus the temperature. The different equations of ${\gamma }_l^{\mathrm{p}}\left(T\right)$ are given in

Table 3. Equations of ${\gamma }_l^{\mathrm{p}}\left(T\right)$ (in mJ/m²) of the various polar solvents adsorbed on the modified copolymers with the linear regression coefficients.

S-DVB
Solvents	$\mathbf{Equation} {\mathit{\gamma }}_{\mathit{l}}^{\mathbf{p}}\left(\mathit{T}\right)$	R2
cyclohexane	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 4 × 10−4 T − 0.116	0.9909
benzene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 3 × 10−5 T − 0.010	0.9911
toluene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.0022 T + 1.048	0.9984
ethyl acetate	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.0251 T + 14.11	0.9999
ethanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.180 T + 90.12	0.9999
n-propanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.063 T + 30.01	0.9905
i-propanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.111 T + 55.49	0.9999
n-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.019 T + 9.124	0.9958
i-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.054 T + 28.21	0.9999
n-pentanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.0032 T + 1.766	0.9995
i-pentanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.020 T + 11.360	0.9994
Pyridine	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.065 T + 33.38	1
Dichloromethane	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.094 T − 33.51	0.9906
1% melamine/S-DVB
Solvents	Equation ${\gamma }_l^{\mathrm{p}}\left(T\right)$	R2
cyclohexane	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 6 × 10−5 T − 0.003	0.9999
benzene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −6 × 10−5 T + 0.035	1
toluene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −8 × 10−4 T + 0.437	0.9999
ethyl acetate	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.004 T + 4.024	0.9999
ethanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.205 T + 105.85	0.9998
n-propanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.122 T + 60.84	0.9992
i-propanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.076 T + 36.61	0.9966
n-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.059 T + 29.78	0.9997
i-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.030 T + 14.080	0.9846
Dichloromethane	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.020 T + 2.037	0.9995
2% melamine/S-DVB
Solvents	Equation ${\gamma }_l^{\mathrm{p}}\left(T\right)$	R2
cyclohexane	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −2 × 10−5 T + 0.013	0.9999
benzene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −3 × 10−5 T + 0.016	0.9999
toluene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −8 × 10−4 T + 0.561	0.9999
ethyl acetate	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.004 T + 3.351	0.9999
ethanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.145 T + 70.16	0.9966
n-propanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.136 T + 66.86	0.9987
i-propanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.147 T + 99.70	0.9999
n-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.088 T + 43.58	0.9989
i-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.097 T + 50.92	1
Dichloromethane	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.037 T − 1.415	0.9995
3% melamine/S-DVB
Solvents	Equation ${\gamma }_l^{\mathrm{p}}\left(T\right)$	R2
cyclohexane	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 2 × 10−4 T − 0.050	0.9977
benzene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.0012 T − 0.452	0.9969
toluene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.0017 T + 0.825	0.9978
ethyl acetate	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.020 T − 4.373	0.9979
ethanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.662 T + 325.2	0.9999
n-propanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.409 T + 197.56	0.999
i-propanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.325 T + 156.67	0.9985
n-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.263 T + 126.86	0.9991
i-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.201 T + 96.57	0.9984
Dichloromethane	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.022 T + 15.682	0.9996
4% melamine/S-DVB
Solvents	Equation ${\gamma }_l^{\mathrm{p}}\left(T\right)$	R2
cyclohexane	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.002 T − 0.587	0.9971
benzene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.002 T − 0.497	0.9978
toluene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.008 T − 2.192	0.9983
ethyl acetate	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.007 T + 4.91	0.9992
ethanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.371 T + 195.72	0.9998
n-propanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.253 T + 139.54	0.9995
i-propanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.210 T + 111.55	0.9997
n-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.154 T + 80.89	0.9997
i-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.124 T + 61.62	1
Dichloromethane	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.057 T − 11.874	0.9973
1% 5-HMU/S-DVB
Solvents	Equation ${\gamma }_l^{\mathrm{p}}\left(T\right)$	R2
benzene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 3 × 10−5 T + 0.008	0.9914
toluene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.043 T + 24.09	0.9891
ethyl acetate	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.036 T − 3.586	0.9981
ethanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.292 T + 140.76	0.9961
i-propanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.090 T + 42.2	0.9287
n-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.210 T + 103.05	0.9992
i-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.124 T + 60.03	0.9973
i-pentanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.121 T + 60.29	0.9998
Dichloromethane	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.005 T + 4.348	0.9983
3.5% 5-HMU/S-DVB
Solvents	Equation ${\gamma }_l^{\mathrm{p}}\left(T\right)$	R2
benzene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 4 × 10−4 T − 0.156	0.9935
toluene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −4 × 10−4 T + 0.542	0.9988
ethyl acetate	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.183 T − 58.14	0.9938
ethanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.248 T + 130.23	0.9997
i-propanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.139 T + 82.08	0.9985
n-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.1274 T + 72.60	0.9983
i-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.105 T + 62.56	0.998
i-pentanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.047 T + 14.09	0.9983
Dichloromethane	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.0070 T + 4.119	0.9998
10% 5-HMU/S-DVB
Solvents	Equation ${\gamma }_l^{\mathrm{p}}\left(T\right)$	R2
benzene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.0017 T − 0.588	0.9942
toluene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.013 T − 3.856	0.9949
ethyl acetate	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.183 T − 59.09	0.9945
ethanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.150 T + 113.86	0.9995
i-propanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.154 T − 9.398	0.995
n-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.097 T + 52.92	0.9993
i-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.162 T − 21.42	0.996
i-pentanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.074 T + 37.042	1
Dichloromethane	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.008 T + 4.491	0.9999
1% 5-FU/S-DVB
Solvents	Equation ${\gamma }_l^{\mathrm{p}}\left(T\right)$	R2
benzene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.0016 T − 0.668	0.9905
toluene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.015 T − 5.243	0.9945
ethyl acetate	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.020 T + 30.52	0.987
ethanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.882 T − 276.34	0.9948
i-propanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.021 T + 76.68	0.8954
n-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.862 T − 304.64	0.9947
i-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.965 T − 334.37	0.995
i-pentanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.520 T + 259.83	0.9995
Dichloromethane	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.001 T + 0.671	0.9858
5% 5-FU/S-DVB
Solvents	Equation ${\gamma }_l^{\mathrm{p}}\left(T\right)$	R2
benzene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 2 × 10−4 T − 0.074	0.9967
toluene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.016 T − 4.833	0.9979
ethyl acetate	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.003 T + 19.418	0.9717
ethanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.175 T + 84.021	0.9983
i-propanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.175 T + 116.52	0.9974
n-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.219 T + 121.67	0.9985
i-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.160 T − 9.321	0.9997
i-pentanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.003 T + 31.15	0.9386
Dichloromethane	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.0002 T + 1.280	0.9714
10% 5-FU/S-DVB
Solvents	Equation ${\gamma }_l^{\mathrm{p}}\left(T\right)$	R2
benzene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 1 × 10−4 T − 0.036	0.9986
toluene	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.063 T − 17.82	0.9988
ethyl acetate	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.073 T + 65.639	0.9991
ethanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.2547 T + 124.57	0.9992
i-propanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.326 T + 211.43	0.9992
n-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.318 T + 176.42	0.9996
i-butanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.192 T + 93.24	0.9989
i-pentanol	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = −0.347 T + 213.6	0.9999
Dichloromethane	${\gamma }_l^{\mathrm{p}}\left(T\right)$ = 0.002 T − 0.057	0.9981

.

Results in Figure S1 and Table 3 highlight the higher dependence of ${\gamma }_l^{\mathrm{p}}\left(T\right)$ both on the temperature and modifier percentage. It was shown that the polar surface energy of ethanol, propanol, i-propanol, n-butanol, i-butanol, and n-pentanol gave the highest values, whereas cyclohexane, benzene, and toluene exhibited the lowest ${\gamma }_l^{\mathrm{p}}\left(T\right)$. The presence of a hydroxyl group in these solvents then strengthens their polarity relative to other polar molecules.

3.4. Work of Adhesion of Organic Solvents on Modified Copolymer

The determination of the London dispersive and polar surface energies of the various modified copolymers and the values of the polar surface energy of adsorbed solvents, using the Equation (12), led to the values of the dispersive $W_a^{\mathrm{d}}\left(T\right)$, polar $W_a^{\mathrm{p}}\left(T\right)$, and total work $W_a\left(T\right)$ of adhesion between solvents and the various solid surfaces by varying the temperature, the modifier, and its percentage. The variations in $W_a^{\mathrm{d}}\left(T\right)$ are plotted in Figure S2 as a function of temperature for all copolymers and modifiers at different percentages. The evolution of $W_a^{\mathrm{p}}\left(T\right)$ versus the temperature is drawn in Figure 3. An excellent linearity of the curves $W_a^{\mathrm{d}}\left(T\right)$ and $W_a^{\mathrm{p}}\left(T\right)$ is observed in Figure S2 and Figure 2 for all solvents and solid materials. A general decrease was noticed against the temperature for the two dispersive and polar works of adhesion with different behaviors depending on the modifier nature and its percentage. It is shown in Figure 3 that the polar adhesion work of ethanol on S-DVB modified by melamine was the highest, while that of benzene and toluene was the lowest, and a minimum polar adhesion has been noticed, confirming the lowest values obtained in the adsorption of these solvents on the modified copolymer. However, in the case of the modification of S-DVB by 5-HMU, the polar work of adhesion $W_a^{\mathrm{p}}\left(T\right)$ of ethyl acetate was the highest for 1% and 3.5% of 5-HMU, while that of i-propanol gave the highest $W_a^{\mathrm{p}}\left(T\right)$ for 10% 5-HMU, 1% 5-FU, and 5% 5-FU. Furthermore, the comparison between the various modifiers led us to conclude using Figure 3 that the maximum adhesion work was obtained with 5-FU. The enhanced adhesion energy observed in the S-DVB copolymer modified by 5-FU can be attributed to several molecular-level mechanisms involving both surface energy modulation and specific intermolecular interactions, detailed as follows:

• Molecular features of 5-fluorouracil. 5-FU is a highly polar molecule characterized by multiple hydrogen bond donors and acceptors, particularly from its amide (C=O) and imine (N–H) groups. The presence of a fluorine atom with strong electronegativity contributed to dipole–dipole interactions and localized electron density. These features enable 5-FU to interact strongly with both the polymer backbone and the adsorbing solvents.
• Surface energy regulation by 5-FU. The incorporation of 5-FU onto the S-DVB surface increases the polar component of the surface energy ${\gamma }_s^p$ through hydrogen bonding and dipole interactions. The overall surface free energy due to enhanced molecular heterogeneity also increases and leads to the increased density of functional groups. This results in stronger intermolecular forces with adsorbed molecules (e.g., polar solvents), thus increasing the work of adhesion. This was particularly observed with 5% 5-FU on S-DVB.
• Mechanism of adhesion energy enhancement. The presence of 5-FU’s amide and imide groups can lead to the formation of strong hydrogen bonds with polar solvents. These hydrogen bonding interactions are directional and cooperative, leading to stable adsorption layers. On the other hand, the C–F bond in 5-FU contributes to a high local dipole moment, enhancing van der Waals dipolar interactions with polarizable solvent molecules. The aromatic ring of 5-FU can engage in π–π stacking with aromatic solvents or even with the S-DVB backbone, stabilizing the surface architecture. The strong polar groups can induce dipoles in non-polar solvent molecules (Debye interactions), contributing further to adhesion.
• Comparison with HMU and melamine. The melamine modifier has multiple amine groups but lacks the C=O/N–H polarity balance and the electronegative substituent that 5-FU has. On the other hand, 5-HMU contains hydroxyl and carbonyl groups but is less electron-withdrawing and lacks the strong dipole moment contributed by fluorine. Thus, while all modifiers increase adhesion relative to unmodified S-DVB, 5-FU offers a unique combination of strong polar interactions and molecular alignment, leading to a higher adhesion energy.

The sum of the two dispersive and polar contributions of the adhesion work led to the determination of the total work of adhesion of the various solvents on the different modified copolymers. The obtained results are given in

Table 4. Equations of total work of adhesion $W_a\left(T\right)$ (in mJ/m²) of the various model organic solvents on S-DVB modified by melamine, 5-HMU, and 5-FU at by different percentages, with the linear regression coefficients, the surface entropy $∆S_S$ (in mJ m⁻² K⁻¹), and the surface enthalpy $∆H_S$ (in mJ m⁻²) of adhesion work, the maximum temperature $T_{Max}=∆H_S/∆S_S$.

S-DVB Copolymer
Solvents	${\mathit{W}}_{\mathit{a}}\left(\mathit{T}\right)$	$∆{\mathit{S}}_{\mathit{S}}$	$∆{\mathit{H}}_{\mathit{S}}$	${\mathit{T}}_{\mathit{M}\mathit{a}\mathit{x}.}$(K)	R2
n-hexane	$W_a\left(T\right)$ = −1.07 T + 513.05	1.07	513.05	477.57	0.9972
n-heptane	$W_a\left(T\right)$ = −0.92 T + 454.45	0.92	454.45	495.64	0.9858
n-octane	$W_a\left(T\right)$ = −0.95 T + 475.17	0.95	475.17	502.61	0.9804
n-nonane	$W_a\left(T\right)$ = −0.99 T + 498.93	0.99	498.93	506.17	0.9778
Benzene	$W_a\left(T\right)$ = −1.10 T + 550.93	1.10	550.93	502.67	0.9812
Toluene	$W_a\left(T\right)$ = −1.29 T + 664.32	1.29	664.32	514.42	0.9754
Ethyl acetate	$W_a\left(T\right)$ = −1.29 T + 669.43	1.29	669.43	518.38	0.9859
Ethanol	$W_a\left(T\right)$ = −1.85 T + 945.32	1.85	945.32	510.21	0.9932
i-Propanol	$W_a\left(T\right)$ = −1.74 T + 891.1	1.74	891.1	511.04	0.9905
Dichloromethane	$W_a\left(T\right)$ = −1.23 T + 654.39	1.23	654.39	531.03	0.9921
1% Melamine/S-DVB Copolymer
Solvents	$W_a\left(T\right)$	$∆S_S$	$∆H_S$	$T_{Max.}$	R2
n-hexane	$W_a\left(T\right)$ = −1.00 T + 480.8	1.00	480.8	479.55	0.9967
n-heptane	$W_a\left(T\right)$ = −0.66 T + 335.68	0.65	335.68	512.65	0.9999
n-octane	$W_a\left(T\right)$ = −0.59 T + 317.85	0.60	317.85	531.17	0.9999
n-nonane	$W_a\left(T\right)$ = −0.58 T + 316.17	0.58	316.17	542.69	0.9999
Benzene	$W_a\left(T\right)$ = −0.71 T + 375.92	0.71	375.92	531.94	0.9999
Toluene	$W_a\left(T\right)$ = −0.57 T + 335.24	0.57	335.24	585.37	0.9999
Ethyl acetate	$W_a\left(T\right)$ = −0.58 T + 319.32	0.58	319.32	554.47	0.9999
Ethanol	$W_a\left(T\right)$ = −0.64 T + 368.46	0.64	368.46	574.46	0.9999
i-Propanol	$W_a\left(T\right)$ = −1.21 T + 668.61	1.21	668.61	553.39	0.9999
Dichloromethane	$W_a\left(T\right)$ = −1.34 T + 662.71	1.34	662.71	494.38	0.9997
2% Melamine/S-DVB Copolymer
Solvents	$W_a\left(T\right)$	$∆S_S$	$∆H_S$	$T_{Max.}$	R2
n-hexane	$W_a\left(T\right)$ = −0.78 T + 372.02	0.78	372.02	477.93	0.9946
n-heptane	$W_a\left(T\right)$ = −0.52 T + 265.41	0.52	265.41	506.89	0.994
n-octane	$W_a\left(T\right)$ = −0.50 T + 260.01	0.50	260.01	520.64	0.9894
n-nonane	$W_a\left(T\right)$ = −0.50 T + 263.73	0.50	263.73	528.73	0.9864
Benzene	Wa = −0.59 T + 308.05	0.59	308.05	519.30	0.9904
Toluene	$W_a\left(T\right)$ = −0.58 T + 324.78	0.58	324.78	563.95	0.9789
Ethyl acetate	$W_a\left(T\right)$ = −0.59 T + 334.41	0.59	334.41	568.34	0.9892
Ethanol	$W_a\left(T\right)$ = −1.5 T + 764.61	1.50	764.61	510.52	0.9983
i-Propanol	$W_a\left(T\right)$ = −1.15 T + 694.21	1.15	694.21	602.30	0.9964
Dichloromethane	$W_a\left(T\right)$ = −0.85 T + 502.92	0.85	502.92	590.42	0.9978
3% Melamine/S-DVB Copolymer
Solvents	$W_a\left(T\right)$	$∆S_S$	$∆H_S$	$T_{Max.}$	R2
n-hexane	$W_a\left(T\right)$ = −0.88 T + 423.69	0.88	423.69	479.34	0.9952
n-heptane	$W_a\left(T\right)$ = −0.60 T + 307.28	0.60	307.28	509.75	0.9954
n-octane	$W_a\left(T\right)$ = −0.56 T + 296.17	0.56	296.17	525.68	0.9917
n-nonane	$W_a\left(T\right)$ = −0.56 T + 297.66	0.56	297.66	535.36	0.9889
Benzene	$W_a\left(T\right)$ = −0.67 T + 355.5	0.67	355.5	529.33	0.9926
Toluene	$W_a\left(T\right)$ = −0.65 T + 363.83	0.65	363.83	557.68	0.9822
Ethyl acetate	$W_a\left(T\right)$ = −0.69 T + 392.76	0.69	392.76	566.75	0.992
Ethanol	$W_a\left(T\right)$ = −2.05 T + 1049.6	2.05	1049.6	511.88	0.9991
i-Propanol	$W_a\left(T\right)$ = −1.72 T + 875.58	1.72	875.58	510.42	0.9983
Dichloromethane	$W_a\left(T\right)$ = −1.12 T + 577.52	1.12	577.52	516.75	0.9985
4% Melamine/S-DVB Copolymer
Solvents	$W_a\left(T\right)$	$∆S_S$	$∆H_S$	$T_{Max.}$	R2
n-hexane	$W_a\left(T\right)$ = −0.96 T + 460.73	0.96	460.73	479.28	0.9952
n-heptane	$W_a\left(T\right)$ = −0.63 T + 323.74	0.63	323.74	511.52	0.9969
n-octane	$W_a\left(T\right)$ = −0.58 T + 308.83	0.58	308.83	528.91	0.995
n-nonane	$W_a\left(T\right)$ = −0.57 T + 308.54	0.57	308.54	539.59	0.9934
Benzene	$W_a\left(T\right)$ = −0.71 T + 377.26	0.71	377.26	535.04	0.9956
Toluene	$W_a\left(T\right)$ = −0.67 T + 394.99	0.66	394.99	594.24	0.9896
Ethyl acetate	$W_a\left(T\right)$ = −0.73 T + 407.05	0.73	407.05	557.37	0.9956
Ethanol	$W_a\left(T\right)$ = −1.78 T + 950.98	1.78	950.98	535.58	0.9993
i-Propanol	$W_a\left(T\right)$ = −1.47 T + 797.06	1.47	797.06	543.18	0.9986
Dichloromethane	$W_a\left(T\right)$ = −1.17 T + 638	1.17	638	545.21	0.9988
1% 5-HMU/S-DVB Copolymer
Solvents	$W_a\left(T\right)$	$∆S_S$	$∆H_S$	$T_{Max.}$	R2
n-hexane	$W_a\left(T\right)$ = −0.79 T + 377.09	0.79	377.09	478.42	0.9996
n-heptane	$W_a\left(T\right)$ = −0.59 T + 297.17	0.59	297.17	503.00	0.9969
n-octane	$W_a\left(T\right)$ = −0.58 T + 298.07	0.58	298.07	514.00	0.9949
n-nonane	$W_a\left(T\right)$ = −0.59 T + 306.26	0.59	306.26	520.14	0.9939
Benzene	$W_a\left(T\right)$ = −0.69 T + 355.57	0.69	355.57	512.20	0.9956
Toluene	$W_a\left(T\right)$ = −1.01 T + 530.27	1.01	530.27	523.16	0.9969
Ethyl acetate	$W_a\left(T\right)$ = −1.08 T + 552.6	1.08	552.6	514.14	0.9991
Ethanol	$W_a\left(T\right)$ = −1.23 T + 617.99	1.23	617.99	501.37	0.9969
i-Propanol	$W_a\left(T\right)$ = −0.98 T + 495.06	0.98	495.06	507.75	0.9897
Dichloromethane	$W_a\left(T\right)$ = −1.26 T + 619.03	1.26	619.03	490.52	0.9023
3.5% 5-HMU/S-DVB Copolymer
Solvents	$W_a\left(T\right)$	$∆S_S$	$∆H_S$	$T_{Max.}$	R2
n-hexane	$W_a\left(T\right)$= −0.80 T + 380.26	0.80	380.26	477.77	0.999
n-heptane	$W_a\left(T\right)$ = −0.66 T + 326.22	0.66	326.22	497.51	0.997
n-octane	$W_a\left(T\right)$ = −0.67 T + 337.84	0.67	337.84	505.37	0.9958
n-nonane	$W_a\left(T\right)$ = −0.69 T + 353	0.69	353	509.53	0.9954
Benzene	$W_a\left(T\right)$ = −0.78 T + 397.1	0.78	397.1	508.39	0.996
Toluene	$W_a\left(T\right)$ = −0.89 T + 471.28	0.89	471.28	526.98	0.9955
Ethyl acetate	$W_a\left(T\right)$ = −0.97 T + 567.37	0.97	567.37	582.46	0.9976
Ethanol	$W_a\left(T\right)$ = −1.66 T + 862.63	1.66	862.63	520.85	0.9992
i-Propanol	$W_a\left(T\right)$ = −1.49 T + 795.55	1.490	795.55	533.78	0.9988
Dichloromethane	$W_a\left(T\right)$ = −0.99 T + 495.17	0.986	495.17	502.00	0.9989
10% 5-hydroxy-6-methyluracil/S-DVB Copolymer
Solvents	$W_a\left(T\right)$	$∆S_S$	$∆H_S$	$T_{Max.}$	R2
n-hexane	$W_a\left(T\right)$ = −0.76 T + 361.98	0.76	361.98	476.48	0.9998
n-heptane	$W_a\left(T\right)$ = −0.70 T + 344.16	0.70	344.16	490.89	0.9996
n-octane	$W_a\left(T\right)$ = −0.75 T + 371.62	0.75	371.62	495.49	0.9993
n-nonane	$W_a\left(T\right)$ = −0.80 T + 396.43	0.80	396.43	497.78	0.9991
Benzene	$W_a\left(T\right)$ = −0.87 T + 438.65	0.87	438.65	502.58	0.9994
Toluene	$W_a\left(T\right)$ = −1.08 T + 562.98	1.08	562.98	522.63	0.9979
Ethyl acetate	$W_a\left(T\right)$ = −1.02 T + 585.03	1.02	585.03	573.90	0.9992
Ethanol	$W_a\left(T\right)$ = −1.71 T + 931.89	1.71	931.89	544.61	0.9998
i-Propanol	$W_a\left(T\right)$ = −1.54 T + 878.5	1.54	878.5	569.09	0.9995
Dichloromethane	$W_a\left(T\right)$ = −1.01 T + 503.78	1.01	503.78	499.09	0.9998
1% 5-Fluouracil/S-DVB Copolymer
Solvents	$W_a\left(T\right)$	$∆S_S$	$∆H_S$	$T_{Max.}$	R2
n-hexane	$W_a\left(T\right)$ = −0.85 T + 409.22	0.85	409.22	480.47	0.9991
n-heptane	$W_a\left(T\right)$ = −0.53 T + 276.42	0.53	276.42	517.25	0.9892
n-octane	$W_a\left(T\right)$ = −0.47 T + 253.35	0.47	253.35	540.65	0.9742
n-nonane	$W_a\left(T\right)$ = −0.44 T + 247.09	0.44	247.09	556.26	0.9622
Benzene	$W_a\left(T\right)$ = −0.56 T + 301.56	0.56	301.56	540.91	0.9769
Toluene	$W_a\left(T\right)$ = −0.48 T + 295.44	0.48	295.44	614.09	0.9325
Ethyl acetate	$W_a\left(T\right)$ = −0.92 T + 507.43	0.92	507.43	554.51	0.9892
Ethanol	$W_a\left(T\right)$ = −1.32 T + 753.74	1.32	753.74	569.94	0.9949
i-Propanol	$W_a\left(T\right)$ = −1.29 T + 716.03	1.29	716.03	556.01	0.9931
Dichloromethane	$W_a\left(T\right)$ = −0.85 T + 432.53	0.85	432.53	508.32	0.997
5% 5-Fluouracil/S-DVB Copolymer
Solvents	$W_a\left(T\right)$	$∆S_S$	$∆H_S$	$T_{Max.}$	R2
n-hexane	$W_a\left(T\right)$ = −0.91 T + 438.27	0.91	438.27	479.61	0.9983
n-heptane	$W_a\left(T\right)$ = −0.60 T + 309.29	0.60	309.29	512.15	0.9978
n-octane	$W_a\left(T\right)$ = −0.55 T + 293.5	0.55	293.5	530.26	0.9956
n-nonane	$W_a\left(T\right)$ = −0.54 T + 292.32	0.54	292.32	541.53	0.9941
Benzene	$W_a\left(T\right)$ = −0.6554 T + 347.96	0.6554	347.96	530.91	0.9961
Toluene	$W_a\left(T\right)$ = −0.6949 T + 415.71	0.6949	415.71	598.23	0.9927
Ethyl acetate	$W_a\left(T\right)$ = −1.2143 T + 693.27	1.2143	693.27	570.92	0.9986
Ethanol	$W_a\left(T\right)$ = −1.7361 T + 880.53	1.7361	880.53	507.19	0.9993
i-Propanol	$W_a\left(T\right)$ = −1.7287 T + 963.71	1.7287	963.71	557.48	0.9991
Dichloromethane	$W_a\left(T\right)$ = −0.9861 T + 507.27	0.9861	507.27	514.42	0.9991
10% 5-Fluouracil/S-DVB Copolymer
Solvents	$W_a\left(T\right)$	$∆S_S$	$∆H_S$	$T_{Max.}$	R2
n-hexane	$W_a\left(T\right)$ = −0.94 T + 451.85	0.94	451.85	479.67	0.9976
n-heptane	$W_a\left(T\right)$ = −0.64 T + 327.09	0.64	327.09	510.76	0.9992
n-octane	$W_a\left(T\right)$ = −0.59 T + 313.4	0.59	313.4	527.52	0.9986
n-nonane	$W_a\left(T\right)$ = −0.58 T + 313.9	0.58	313.9	537.68	0.9981
Benzene	$W_a\left(T\right)$ = −0.70 T + 369.84	0.70	369.84	528.04	0.9987
Toluene	$W_a\left(T\right)$ = −0.77 T + 484.8	0.77	484.8	627.41	0.9978
Ethyl acetate	$W_a\left(T\right)$ = −1.28 T + 744.91	1.28	744.91	581.55	0.9996
Ethanol	$W_a\left(T\right)$ = −1.77 T + 912.74	1.77	912.74	515.38	0.9998
i-Propanol	$W_a\left(T\right)$ = −1.80 T + 1031.2	1.80	1031.2	572.89	0.9997
Dichloromethane	$W_a\left(T\right)$ = −0.93 T + 478.52	0.93	478.52	514.04	0.9993

in the form of the following equations: $W_a\left(T\right)$ function of temperature, modifier, and its percentage. Two new thermodynamic parameters were defined. The first one is the surface entropy $∆S_S$ of adhesion work and the second is relative to the surface enthalpy $∆H_S$ of adhesion work. The general equation of $W_a\left(T\right)$ can be written as follows:

$$W_a\left(T\right)=∆H_S-T∆S_S$$

(19)

The values of $∆H_S$ and $∆S_S$ of the different organic solvents given in Table 4 for the modified copolymers at different modifier percentages led to linear relations between these surface parameters and the corresponding percentage ($q$) of melamine (noted Mela), 5-HMU, and 5-FU. The equations of $∆H_S\left(q\right)$ and $∆S_S\left(q\right)$ relative to the work of adhesion on the modified copolymers are given in

Table 5. Equations of the surface adhesion parameters $∆H_S\left(q\right)$ and $∆S_S\left(q\right)$ of the different solvents on the modified copolymers as a function of modifier percentage with the linear regression coefficients.

S-DVB Copolymer
Solvents	$\mathbf{Equation} ∆{\mathit{S}}_{\mathit{S}}\left(\mathit{q}\right)$ (in mJ m−2 K−1)	R2	$\mathbf{Equation} ∆{\mathit{H}}_{\mathit{S}}\left(\mathit{q}\right)$ (in mJ m−2)	R2
n-hexane	$∆S_S$ = 0.076 q (Mela) + 0.65	0.9757	$∆H_S$ = 46.92 q (Mela) + 277.19	0.9948
n-heptane	$∆S_S$ = 0.033 q (Mela) + 0.615	0.9945	$∆H_S$ = 33.70 q (Mela) + 196.20	0.9699
n-octane	$∆S_S$ = 0.024 q (Mela) + 0.485	0.9931	$∆H_S$ = 24.44 q (Mela) + 215.01	0.9701
n-nonane	$∆S_S$ = 0.016 q (Mela) + 0.51	0.9143	$∆H_S$ = 22.05 q (Mela) + 223.96	0.9647
Benzene	$∆S_S$ = 0.065 q (Mela) + 0.46	0.9837	$∆H_S$ = 34.78 q (Mela) + 242.54	0.9821
Toluene	$∆S_S$ = 0.031 q (Mela) + 0.545	0.9468	$∆H_S$ = 30.83 q (Mela) + 270.14	0.9852
Ethyl acetate	$∆S_S$ = 0.055 q (Mela) + 0.51	0.9181	$∆H_S$ = 32.15 q (Mela) + 283.00	0.9313
Ethanol	$∆S_S$ = 0.235 q (Mela) + 0.97	0.9612	$∆H_S$ = 193.26 q (Mela) + 225.28	0.9515
i-Propanol	$∆S_S$ = 0.146 q (Mela) + 1.04	0.9769	$∆H_S$ = 101.67 q (Mela) + 517.19	0.9238
Dichloromethane	$∆S_S$ = −0.09 q (Mela) + 1.41	0.962	$∆H_S$ = 60.23 q (Mela) + 394.56	0.9885
S-DVB/5-HMU
Solvents	Equation $∆S_S\left(q\right)$ (in mJ m−2 K−1)	R2	Equation $∆H_S\left(q\right)$ (in mJ m−2)	R2
n-hexane	$∆S_S$ = −0.003 q (5-HMU) + 0.793	0.9963	$∆H_S$ = 1.15 q (5-HMU) + 376.06	0.9992
n-heptane	$∆S_S$ = 0.011 q (5-HMU) + 0.592	0.9106	$∆H_S$ = 3.98 q (5-HMU) + 306.11	0.9177
n-octane	$∆S_S$ = 0.018 q (5-HMU) + 0.582	0.9209	$∆H_S$ = 7.58 q (5-HMU) + 299.23	0.9137
n-nonane	$∆S_S$ = 0.022 q (5-HMU) + 0.589	0.9508	$∆H_S$ = 9.35 q (5-HMU) + 306.71	0.9276
Benzene	$∆S_S$ = 0.019 q (5-HMU) + 0.689	0.9382	$∆H_S$ = 8.66 q (5-HMU) + 355.24	0.9383
Toluene	$∆S_S$ = 0.02 q (5-HMU) + 0.88	0.9999	$∆H_S$ = 3.55 q (5-HMU) + 527.96	0.9914
Ethyl acetate	$∆S_S$ = −0.006 q (5-HMU) + 1.080	0.9382	$∆H_S$ = 3.43 q (5-HMU) + 551.78	0.9606
Ethanol	$∆S_S$ = 0.050 q (5-HMU) + 1.233	0.9261	$∆H_S$ = 33.10 q (5-HMU) + 610.84	0.9582
i-Propanol	$∆S_S$ = 0.033 q (5-HMU) + 1.205	0.9999	$∆H_S$ = 39.70 q (5-HMU) + 497.81	0.9249
Dichloromethane	$∆S_S$ = −0.026 q (5-HMU) + 1.254	0.9008	$∆H_S$ = −12.08 q (5-HMU) + 620.49	0.9479
S-DVB/5-FU
Solvents	Equation $∆S_S\left(q\right)$ (in mJ m−2 K−1)	R2	Equation $∆H_S\left(q\right)$ (in mJ m−2)	R2
n-hexane	$∆S_S$ = 0.010 q (5-FU) + 0.848	0.9368	$∆H_S$ = 4.65 q (5-FU) + 408.29	0.9286
n-heptane	$∆S_S$ = 0.012 q (5-FU) + 0.526	0.9523	$∆H_S$ = 5.55 q (5-FU) + 274.69	0.9462
n-octane	$∆S_S$ = 0.013 q (5-FU) + 0.467	0.9368	$∆H_S$ = 6.56 q (5-FU) + 251.75	0.9357
n-nonane	$∆S_S$ = 0.015 q (5-FU) + 0.439	0.9089	$∆H_S$ = 7.30 q (5-FU) + 245.52	0.9311
Benzene	$∆S_S$ = 0.015 q (5-FU) + 0.557	0.9286	$∆H_S$ = 7.46 q (5-FU) + 300.03	0.9296
Toluene	$∆S_S$ = 0.032 q (5-FU) + 0.478	0.9026	$∆H_S$ = 20.74 q (5-FU) + 288.02	0.9529
Ethyl acetate	$∆S_S$ = 0.026 q (5-FU) + 1.037	0.9126	$∆H_S$ = 25.73 q (5-FU) + 511.32	0.8628
Ethanol	$∆S_S$ = 0.049 q (5-FU) + 1.312	0.9243	$∆H_S$ = 11.00 q (5-FU) + 809.76	0.9292
i-Propanol	$∆S_S$ = 0.056 q (5-FU) + 1.284	0.9141	$∆H_S$ = 23.48 q (5-FU) + 811.75	0.9257
Dichloromethane	$∆S_S$ = 0.019 q (5-FU) + 0.892	0.9999	$∆H_S$ = 5.08 q (5-FU) + 428.94	0.9898

with the linear regression coefficients. The results in Table 5 led to the following general equations:

$$∆H_S\left(q\right)=aq+b$$

(20)

$$∆S_S\left(q\right)=cq+d$$

(21)

where $a$, $b$, $c$, and $d$ given in Table 5 are constant coefficients, depending on the work of adhesion of the solvents on the modified S-DVB.

The results presented in Table 5 show that the linearity of the variables $∆H_S\left(q\right)$ and $∆S_S\left(q\right)$ is not perfectly satisfied for all solvents, where the linear regression coefficients were found to be relatively low (around 0.9000). However, the general tendency of the linearity of $∆H_S\left(q\right)$ and $∆S_S\left(q\right)$ is satisfied for most solvents (about 90%) and solid materials. The relative weakness in the linearity of $∆H_S\left(q\right)$ and $∆S_S\left(q\right)$ shown in Table 5 for certain solvents is certainly due to the accumulation of uncertainties, beginning from the chromatographic measurements of the retention time, the free energy, and the values of $∆H_S\left(q\right)$ and $∆S_S\left(q\right)$, until the work of adhesion $W_a\left(T,q\right)$. The uncertainty about the retention time was about 1%, but other sources of uncertainty were made from other experimental parameter values such as the dispersive and polar free energies of adsorption, the London dispersive and polar surface energy of copolymers, and the work of adhesion.

The combination of Equations (14)–(16) led to a universal equation giving the work of adhesion $W_a(T,q)$ of an organic solvent on a copolymer, modified by a modifier percentage $q$:

$$W_a\left(T,q\right)=aq+b-T(cq+d)$$

(22)

$W_a\left(T,q\right)$, given by Equation (22), is a function of two variables, $T$ and $q$.

The above equation represents a quantification of the work of adhesion, when the temperature and the modifier percentage are known. This result is similar to that obtained in previous studies during the study of the adsorption of PMMA on silica and alumina at different recovery fractions, where the polar free energy of adsorption was correlated to the two thermodynamic variables such as the temperature and the percentage of adsorption. Another interesting result was obtained from Table 5 by drawing the variations in $∆H_S$ and $∆S_S$ of the different modified copolymers. The linear relation of the surface enthalpy of adhesion work $∆H_S(∆S_S)$ was obtained versus the surface entropy for the different copolymers, and a new surface temperature $T_S$ was defined. This new variable constitutes a real characteristic of the copolymer. The linear equations are given in

Table 6. Equations of $∆H_S$ as a function of $∆S_S$ of the different modified copolymers with the values of $T_S$ and the corresponding linear regression coefficients.

Copolymer	$\mathbf{Equations} ∆{\mathit{H}}_{\mathit{S}}=\mathit{f}(∆{\mathit{S}}_{\mathit{S}})$	${\mathit{T}}_{\mathit{S}}$	R2
S-DVB Copolymer	$∆H_S$ = 527.12 $∆S_S$ − 23.502	527.12	0.9923
1% Melamine/S-DVB Copolymer	$∆H_S$ = 476.71 $∆S_S$ + 42.251	476.71	0.9672
2% Melamine/S-DVB Copolymer	$∆H_S$ = 543.47 $∆S_S$ − 1.841	543.47	0.9596
3% Melamine/S-DVB Copolymer	$∆H_S$ = 500.3 $∆S_S$ + 18.342	500.3	0.9957
4% Melamine/S-DVB Copolymer	$∆H_S$ = 532.74 $∆S_S$ + 1.972	532.74	0.9882
1% 5-HMU/S-DVB Copolymer	$∆H_S$ = 494.38 $∆S_S$ + 9.860	494.38	0.9917
3.5% 5-HMU/S-DVB Copolymer	$∆H_S$ = 546.19 $∆S_S$ − 25.452	546.19	0.9838
10% 5-HMU/S-DVB Copolymer	$∆H_S$ = 609.06 $∆S_S$ − 86.224	609.06	0.9884
1% 5-Fluouracil/S-DVB Copolymer	$∆H_S$ = 558.33 $∆S_S$ − 11.407	558.33	0.9793
5% 5-Fluouracil/S-DVB Copolymer	$∆H_S$ = 534.46 $∆S_S$ − 0.318	534.46	0.9803
10% 5-Fluouracil/S-DVB Copolymer	$∆H_S$ = 556.11 $∆S_S$ − 14.185	556.11	0.973

.

The various equations presented in Table 6 can be generally described by the following equation for all materials:

$$∆H_S=\alpha ∆S_S+\beta$$

(23)

where the slope $\alpha$ represents an isokinetic surface temperature $T_S$ ($T_S=\alpha$) at which all processes in the series of organic solvents proceed with the same work of adhesion, here given by the constant parameter $\beta$. This interesting equation traduces the surface enthalpy–surface entropy compensation with an excellent linear regression coefficient for all studied copolymers.

4. Conclusions

A new method was proposed to determine the variations in the work of adhesion $W_a\left(T\right)$ of model organic solvents on S-DVB copolymers modified by melamine, 5-HMU, and 5-FU at different percentages by varying the temperature. The surface properties of modified copolymers such as the dispersive and polar free energy of adsorption and the London dispersive and polar surface energies of copolymers were used to determine the dispersive $W_a^{\mathrm{d}}\left(T\right)$ and polar $W_a^{\mathrm{p}}\left(T\right)$ works of adhesion of the various organic model solvents on S-DVB copolymers as a function of temperature and modifier percentage. Results showed an excellent linearity of $W_a^{\mathrm{d}}\left(T\right)$ and $W_a^{\mathrm{p}}\left(T\right)$ as a function of temperature for all solvents and copolymers, with a decrease in the temperature depending on the modifier’s nature and its percentage. The highest polar adhesion work was obtained with ethanol on S-DVB modified by melamine, while the values of $W_a^{\mathrm{p}}\left(T\right)$ of benzene and toluene were the lowest. The comparison between the various modifiers led to the conclusion that the maximum adhesion work was obtained with 5-FU on the S-DVB copolymer. Indeed, the modification of S-DVB by 5-FU with high-energy interaction sites increases compatibility and adhesion with a wide range of solvents. This shows that the careful selection of modifiers with tailored molecular functionalities can effectively regulate the polar surface energy and adhesion behavior. The work of adhesion was correlated to the surface enthalpy $∆H_S$ and entropy $∆S_S$ of organic solvents adsorbed on copolymers at different modifier percentages ($q)$ via the following equation:

$$W_a\left(T,q\right)=∆H_S\left(q\right)-T∆S_S\left(q\right)$$

(24)

It was proved that $∆H_S\left(q\right)$ and $∆S_S\left(q\right)$ linearly varied as a function of the modifier percentage ($q)$. The results in Table 5 led to the following general equations:

$$∆H_S\left(q\right)=aq+b$$

(25)

$$∆S_S\left(q\right)=cq+d$$

(26)

A new relation of the work of adhesion $W_a(T,q)$ function of the two variables $T$ and $q$ was therefore proposed:

$$W_a\left(T,q\right)=aq+b-T(cq+d)$$

(27)

Furthermore, linear relations of the surface enthalpy of adhesion work $∆H_S$ as a function of the surface entropy of adhesion were obtained and a new surface temperature $T_S$ representing an isokinetic surface temperature was defined.